Our strategy will be to generalise the concept of frame functions
to GPTs in order to investigate whether they are in exact correspondence
with the objects that represent states in these theories. The main
result of this paper is a proof that the correspondence continues
to hold if and only if the state and effect spaces of a GPT satisfy
the no-restriction hypothesis [1]}, [2]},
or a “noisy” version thereof (see Theorem REF ,
Section REF ). In other words, we
identify exactly all general probabilistic theories which admit a
Gleason-type theorem.
